Self-Observation Impossibility in Complete Quantum Systems: A No-Go Theorem for Observer Closure

We prove that no map satisfying three operationally motivated requirements---definiteness (observation produces a classical record), record stability (observation cannot render a classical record indefinite), and linearity (the map acts linearly on the operator algebra)---can consistently observe the complete state of the system containing it. The proof is short; the contribution is layered. First, the assumption set is strictly weaker than the projection postulate and the Lüders rule, so the result subsumes Breuer's 1995 self-measurement no-go from a smaller axiomatic base. Second, and more importantly, the conclusion is constructive: where Breuer establishes an epistemic limitation on internal state-assignment, we establish an ontological requirement on the location of definite-outcome-producing capacity. A composite-closure lemma extends the result up the observer hierarchy and forbids mutual-observation fixed points, converting the diagnostic disjunction of Frauchiger and Renner (2018) into a directed conclusion: consistent observation of a complete quantum system requires an observer external to that system, and no finite arrangement of mutual observers closes the recursion.